# Kinematic Of Robotic Arms Computer Science Essay

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Nowadays, sophisticated and special-purpose machines that are designed to act pre-specified functions are essential role to perform most automated manufacturing jobs. Therefore, in many assembly and manufacturing functions and tasks, the computer-controlled manipulators are used because of the time saving and cost-effective and complex jobs and manufactures have applied the industrial robot as general-purpose manipulators to perform better for operation in machine and production tools.

The study of kinematic behavior is concerned with designing and modeling a robot, and the motion of robot without thinking forces that produce the motions is involved in a kinematic model. Moreover, the geometric and time based properties for joints and links of a robot with respect to one another is important in robotic arm's kinematics. The main problem in modeling and applying of kinematics is classified into two problems, and one of the problems is forward and direct kinematics which is needed to solve the position of the Cartesian and a mechanism orientation. Another is Inverse Kinematics (IK) calculating the joint variables with the help of information of end-effector position of a robot and orientation. But IK problem is more sophisticated than forward and direct one. The forward kinematics model is applied by using toolbox of robotics for Matlab program whereas IK has been validated on an actual robotic arm.

The number of joints in the manipulator is equal to the number of degrees of freedom (DOF) of a manipulator of open chain and joint variables can be referred as angles depending on the types of joints.

## Types of robots with arms

Cartesian robot/Gantry robot

Cylindrical robot:

Spherical robot / Polar robot

SCARA robot:

Articulated robot

Parallel robot

Anthropomorphic robot

## Manipulator

A human arm has 7 degree of Freedom, 3 DOFs in the wrist and 4 DOFs( in Fig.1) in the arm but in industrial and automated manipulators, they have existing 6 DOFs so that it can be seen that one additional DOF is found in human arm in the wrist position and arbitrary orientation. The number of command axes is equal to the number of robotics joints. In command axes, there are 3 displacements and rotations which fulfill the position and orientation .Fig 3 illustrates a typical robot arm .For human, the extra degree of freedom is able to perform the hand to get a required position and orientation with various different reaching points and arm configurations that are not accessible by only 6 DOFs.

In Fig. 4, a simple model of robot manipulator with only 6 DOFs is shown, where θ7 is removed and θ5 and θ6 have been interchanged so that θ5 and θ6 are same as the mechanical wrists' last two joints .In the complete robotic arm , removing degrees of freedom are applied in an useful way - avoiding obstacle, optimization purposes and limitations in joint motions.

## Work Space of Manipulator

In a manipulator, the workspace is the set of configurations of all end-effector. And the workspace is applied in managing and planning a task for manipulators which means that the manipulator motions must stay within the workspace which can be determined with information about Range Of Motion (ROM) of joints and lengths of robot's links .The robot workspace can be determined by matlab and calculated mathematically with these information of each joint of robotic arm. Figures 5 and 6 show the workspace in XY and YZ coordinates .As show in Figure 1, the robotic arm is at workspace circular radius of 280 mm.

## Basic Geometries of Manipulator

In a robot arm, base part, gripper, links and joints are parts for motion and rotation .The motors and hydraulic actuators are used to control and actuated the joints while a fixed relationship is maintained by the links between the joints. There are two types of joints, including two kinds of motion. A revolute joint which is same as human elbow allows rotary motion in an rotational axis, and a prismatic joint (e.g; telescoping automobile antenna) is the motion of telescopic and extensions. There are some sorts of manipulator kinematics below.

## Open and Closed Chain Manipulator Kinematics

In an open chain manipulator kinematics, a manipulator's mechanics can be described as a kinematic chain of links that are connected by prismatic or revolute joints. One end of the chain is connected to a base and an end effector is fixed to the other end of the chain.Composition of the elementary motions of each link with respect to previous one obtain the resulting motion and then all joints are controlled individually.

In closed chain manipulator, it is much more difficult than open chain manipulator as statics, constraints from other links should be taken into account. One of examples of close chain is parallel robot .The best example of this type of robots is steward platform.

## Forward Kinematic Model

The problem of a robot arm can be solved by various methods, but most commonly used methods are based on Denavit-Hartenberg (DH) parameters and screw displacements which are most suitable for modeling serial manipulators .Some researchers also frequently applied in geometric methods for serial manipulators of simple geometry. DH method is widely used to develop robot's kinematic model because it is versatile and acceptable for links of a serial manipulator and modeling of any number of joints. Figure shows the kinematic model of the robotic arm .The first three joints are for moving the tool points to its required postion and the orientation of the end-effector is adjusted by the last two joints.

## Inverse Kinematic Model

Inverse kinematic model is very useful in application for practical robot system and it computes the required joint angles to get orientation and position. Moreover, IK is also important in other fields-3D games. Compare to forward kinematics, IK does not have an exact and unique solution ensuring minimum joint motion and collision-free operation are taken into account. Analytical approach shall be followed to develop model ED7220C to ensure that correct joint angles are determined by this model for any object within workspace of robotic arm. The four angles, waist θ1, shoulder θ2 , elbow θ3 and tool pitch θ4 are calculated while the desired orientation for object orientation gives tool roll θ5.

The IK model is applied in the real robotic arm manipulator .For example, an object is placed in at given orientation and position and with this information by a user, the developed algorithm, which can provide the solutions to a good degree of accuracy, is used to inspect whether this object lies inside the workspace of the robot .Unless the object is inside the work envelope, the algorithm will terminate after prompting user. The required joint angles that point the end-effector are calculated by using IK model. Last, the command is executed by the Kernel based instructions to move the motors as per mapped encoder tricks. The user provides the object coordinates so that the robot manipulator can move as per computed joint angle.

## Fig.12. IK model application

There are three main methods to solve kinematics-algebraic, geometric and iterative which are shown below.

Algebraic: It is essential to solve equations, q1 , q2 ,…, qN for n degrees of freedom algebraically. The problem can be formulated as :

where the desired orientation and position of the end-effector is described in right-hand side and N stands for N unknowns. But this method is not exact solution for a given manipulator so that a generalized closed-form solution derived for 6 or less DOF chain of kinematic is proposed by Craig ,Manocha and Zhu.

Geometric: In contrast to algebraic method, a closed form solution with the help of the geometry of the manipulator is derived. Lee applied theorems in coordinate geometry to derive and find solutions which include the link coordinate frame on the Xi-1 and Yi-1 for a six DOF manipulator .That method is used in any manipulator with known geometry. The restriction is that the closed-form solution for first three joints of the manipulator must be within in geometric. Another problem is that if other manipulators lie in different geometries, the closed-form solution for one class of manipulators cannot be applied.

Iterative: Iterative method is very important in solving inverse kinematics for joint angles. One of the advantages of this method is converging to one solution. The pseudo-inverse, minimization, and Jacobian methods are constitute iterative methods.

The computational requirements are not dependent on the number of degrees of freedom for robotic arm, but they are usually based on the architecture of network.

## Cooperative Robotic and multi-arm systems

In the last decade, the use of multi-arm systems over the single-arm systems is known to be a key factor as they can perform high flexibility and productivity of workcells. Research efforts in the field of multi-arm systems and cooperative manipulation have been concerned on task description, load distribution and motion/force control.

In an automatic disassembly workcell, two manipulators, a tool changer, a rotating table and a deposit zone is shown. The disassembly task is classified into subtasks that can be achieved either in a parallel way (robots which perform jobs in the same area have independent goals) or in a cooperative way ( robots that work simultaneously on the same object).Some of the dual-arm system is applied to measure the radioactivity intensity of the dismissed reactor's waste: one arm calculates the measurement via probe and the other grasps the waste to maintain probe perpendicular to the surface and at a constant distance.

A flexible laser welding system is used in dual-arm configuration, where the handling robot holds and carries the object while a second robot carries the welding tool so that objects and parts can be cut or welded in the most inaccessible places. In a cooperative system, two robots work in a cooperative way to handle and work large and heavy metal plates and each robot has own controller and communicates each other via a high speed local Ethernet network. Individual robots' motion programming is not necessary but only that of the workpiece or parts shall be handled.

Cooperative tasks programming is not handled in a centralized way in multi-arm industrial workcells, i.e., by installing program and do programming the job at the workpiece level and relying on the overall cooperative task's automatic decomposition in motion primitives for the single arms. Ad-hoc methods are usually applied where the geometry of the workcell/task is used to to program the single robots' path and achieve motion synchronization.

## Fig.13.A cooperative robotic workcell comprised of two Comau Smart Six industrial robots and a sliding track

Hence programming of cooperative tasks (e.g cooperative transportation of heavy loads grasped by multiple robots) becomes very time consuming and cumbersome. When changes in workcell setting occur, there is more problematic (e.g., variation of the programmed paths, change of end-effector tools, addition or elimination of robots).Therefore, re-programming of the single robots is necessary. Moreover, recovery from production stops (e.g., failing device or processing) becomes very complicated if a centralized description of the coordinated task to be restarted is not applied.

Coordination is done by defining each robot's coordinate tool frame as the workpiece is fixed and help by the positioning device: if the workpiece moves, the other robots also move in coordinaton and an effective handling of recovery from failures is also given .But the multimove environment cannot be used well for job planning directly in terms of suitable defined cooperative task-space variables. The approach is for reducing sophisticated cooperative task programming by doing changes the programming effort at the centralized

cooperative task level which means that the user needs to specify the tasks in terms of cooperative task-space variables, while judging the the motion of the single arms in the system is within the planning software.

## Fig.14. Multi-robot wrokcell configuration

Firstly, a taxonomy of cooperative multi-arm systems must be concerned to devise a set of task-space variables. Generally, a robotic workcell is made of positioners( elements which move the workpiece) and workers ( elements that execute the job on workpiece). Workers are robotic manipulators in a traditional workcell, but positioners are specialized equipments and devices which means that if a new task is needed to be executed, rebuilding of the workcell is also essential.

Reusability and flexibility of a workcell can be achieved when robotic arms or multi-purpose articulated devices replace some specialized elements. That class of multi-robot cooperative cell can be referred to as hyper-flexible multi-robot workcells (Fig. 14 ). In the hyper-flexible multi-robot workcells, it is composed of two cooperative COMAU Smart Six robot which are mounted on a sliding track and because of this sliding track,this can be known as kinematically redundant configuration .14 degrees of freedom characterizes the whole system ;the first step is to achieve the objective task of an effective job planning method and defines a set of motion variables which describe a general cooperative task suitably.

Furthermore, consideration of motion planning and task planning for multi-robot cooperative workcells is proposed, based on the formulation of the devised task. Figures 15 and 16 show the overall planning system architecture which is classified as two subsystems, cooperative planner and arm planner.

## Cooperative planner

Cooperative planner subsystem is used to define the cooperative task-space trajectory in terms of meaningful variables which describe the cooperative jobs; by applying the kinematic relationships between the task-space motion variables of the single arms. And motion references for each arm and the cooperative task-space motion variables are calculated and managed. For each cell workcell configuration, the variables that are needed to define the cooperative task are identified and kinematic relationships are also needed to calculate the motion variables of each robotic arm for derivation. Cooperative planner uses these relationships to compute the Cartesian motion references for single arms and devices which compose the workcell.

## Arm Planner

The cartesian motion references from the cooperative is received by the arm planner of each robot in the system and calculating the corresponding joint trajectories via arm inverse kinematics. There are two situations for inverse kinematics by the arm planner to calculate.

During trajectory generation, for solving dynamic and kinematic constraints as well as to achieve trajectory scaling; before the commanded motion starts, that computation should be done.

Also, during measuring and computing the actual joint references for joint control loops from cartesian trajectory; this computation is completed in real time when the arm moves.

## Conclusion

In the robotic kinematics, by controlling links and joints, the gripper can be moved and rotated where we want. To do this purpose, using homogeneous transformations, links and motions shall be accepted to compute coordinate system. Robot kinematics are classified into two types, forward kinematic and inverse kinematic. Direct kinematics includes to solve the forward transformation to compute and find the location of the robot hand in terms of displacements and angles between the links and joints. For Inverse kinematics, this involves to cope the inverse transformation equation to look for the relationships between the links of the manipulator from location of the hand in workspace.

Moreover, cooperative job planning for multi-arm robotic workcells has been achieved and task formulation for cooperative multi-arm tasks, a motion planning is devised. The correct joint angles have been provided by the inverse kinematic model which are implemented on the real robotic platform in order to move the arm gripper to any orientation and position with the robot's workspace.